Question

A 5 kg block is hanging at rest from a spring of k= 10 N/m. Find the work done by an external agent to displace the block down by 10cm at constant negligible speed. Take g= 10m/sec².​

Answer 1

Answer:

the natural words for example the land air and water in which people and animal plant live the natural words for example the land air and water in which people and animals plant live

Answer 2

Answer:

☆Concept:

▪︎if during displacement the block has constant negligible speed that means its change in kinetic energy from initial to final is zero.

▪︎total forces acting on the block:

1. force by gravity(mg)
2. restoring force by spring(kx)
3. force by external agent

▪︎work is said to be negative if opposite in the direction of motion.

☆Work-Energy theorem:

$\boxed{\bf{Work_{total} = KE_{f}-KE_{i}}}$

☆Solution:

》taking all in SI units.

$\rightarrow{\sf{Work_{total} = KE_{f}-KE_{i}}}$

$\rightarrow{\sf{W_{mg}+W_{spring}+W_{F} = 0}}$

$\rightarrow{\sf{mg(h)- \dfrac{1}{2}Kx^{2}+W_{F} = 0}}$

$\rightarrow{\sf{mg(h)+W_{F} = \dfrac{1}{2}Kx^{2}}}$

$\rightarrow{\sf{W_{F} = \dfrac{1}{2}Kx^{2}-mgh}}$

$\rightarrow{\sf{W_{F} = \dfrac{1}{2}(10)(0.1)^{2}-5(10)(0.1)}}$

$\rightarrow{\sf{W_{F} = \dfrac{1}{20}-5}}$

$\rightarrow{\bf{W_{F} = -4.95J}}$

☆☆here,the work done by external agents is negative, that means as we release the block from rest ,the gravity suddenly accelerates it..but to keep the block moving at negligible speed we have to apply upward force,which is opposite to the direction of motion.

---------